It’s All Connected: The Power of Representation to Build Algebraic Reasoning, Middle and High School


It's All Connected focuses on the power of representation to build algebraic reasoning, offering a collection of 40 quick lessons (each takes less than thirty minutes). The lessons feature:

  • creative exercises that illustrate key concepts associated with the graphical representation of functions;
  • reproducible pages on which students can record their work (download provided upon purchasing this resource);
  • correlations to the Common Core State Standards;
  • teaching insights, and more.

Common Core State Connections:
In line with the Common Core State Standards, the lessons in this resource require students to understand and select appropriate units of measurement, to represent and interpret patterns with graphs, and to use graphical representations to model and interpret physical phenomena. In addition, the lessons incorporate all of the mathematical practices outlined in the Common Core State Standards.

Frances Van Dyke
208 Pages

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Frances Van Dyke is an Associate Professor at American University in Washington, DC, where she teaches courses in mathematics and mathematics education. She was also an associate professor at Central Connecticut State University where she taught for ten years. Franny completed her undergraduate degree at Vassar College, a Master of Arts in Teaching: Mathematics, at the University of Chicago, and her doctorate degree in Mathematics from the University of Illinois at Chicago. She is the author of A Visual Approach to Algebra (Dale Seymour, 1998) and A Visual Approach to Functions (Key Curriculum Press, 2002).

"Functions, and their representation by graphs, tables of values, and symbolic expressions, are among the most valuable tools of pure and applied mathematics. Based on extensive study of the challenges in learning about functions, It's All Connected is a valuable resource of easy-to-use activities that teachers in middle and high school mathematics will be able to apply in a variety of ways to develop and deepen key understandings and skills."

James Fey
Professor Emeritus, University of Maryland

"I am always searching for new and exciting ways to present algebraic concepts to my students—It's All Connected does just that. The resource offers a series of fifteen- to twenty-minute simple step-by-step lessons that easily can be incorporated into a larger curriculum or used on their own. The lessons make use of real-world applications that students will enjoy exploring, from the analysis of how rumors spread to the value of a motorcycle. It's All Connected also provides an excellent connection to the Common Core State Standards for modeling relationships through tables and graphs."

Beth Klingher
Math teacher
New Haven Public Schools, Connecticut

"It's All Connected offers a fresh, unique approach to critical algebra concepts. With short, easy-to-use lessons, students can build conceptual understanding of graphs and related representations, beginning with intuitive descriptions and building toward equations. This could be particularly helpful for students who are visually oriented."

Linda Dager Wilson, Director
Green Schools Project
Washington DC

"Teachers committed to implementing the Common Core State Standards for Mathematical Practices will find It's All Connected of enormous value in understanding the role that context and relationships play in student learning. Van Dyke presents a collection of well-crafted, focused lessons with a unique approach to multiple representations for learning key ideas in algebra. Lessons are developed with an eye on both the learning progression and the mathematical horizon."

M. Alejandra SortoAssociate Professor
Department of Mathematics Texas State University
San Marcos, Texas
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